From the viewpoint of the data recording/reproduction principle, a Holographic Digital Data Storage (HDDS) system is typically a page-oriented memory using a volumetric hologram principle. An HDDS system can implement a super high input/output speed of 1 Gbps or above by using a parallel data processing scheme as an input/output scheme, and can be constructed without a mechanical driving unit to thereby implement a very fast data access time of 100 μs or less. And accordingly, the HDDS system has attracted attention as an advanced memory device.
In the meantime, the HDDS system detects and decodes a page-based information image, recorded on a storage medium, using a CCD at the time of reproduction. In this case, in order to decode page-based image data, i.e., binary pixel data, reproduced from the storage medium into original data, one-to-one (1:1) matching signal processing is performed by a CCD, etc. That is, the pixels of the image reproduced from the storage medium and the pixels of the CCD array are matched with each other in a one-to-one manner, thus reproducing original pixel data.
However, a shift multiplexing system using the above-described 1:1 pixel matching is problematic in that there occurs serious degradation of data detected in a CCD array in case a misalignment between a data pixel and a CCD pixel reaches approximately ½ of the size of the CCD pixel.
In order to solve this problem, a conventional method of inversely calculating an ON or OFF level of a Spatial Light Modulator (SLM) by using the inverse transformation of an optical model on the basis of the optical model to thereby correct misaligned pixels has been proposed by Burr of IBM. In the method proposed by Burr, if a Point Spread Function (PSF) is assumed to be a sinc function, an optical field h(x) through the SLM (whose fill factor is ffs) can be expressed in Equation 1 when the width of a Fourier transform aperture is D and the width of a Nyquist aperture is DN.
                              h          ⁡                      (            x            )                          =                  c          ⁢                                    ∫                                                -                                      ff                    d                                                  /                2                                                              ff                  d                                /                2                                      ⁢                          sin              ⁢                                                          ⁢                              c                ⁡                                  (                                                            D                                              D                        N                                                              ⁢                                          (                                              x                        -                                                  x                          ′                                                                    )                                                        )                                            ⁢                                                          ⁢                              ⅆ                                  x                  ′                                                                                        Equation        ⁢                                  ⁢        1            
In this case, if it is assumed that the intensities of signals transmitted from the SLM are p0, p1, and p2, as shown in FIG. 1, and the point spread function (PSF) does not spread a beam above a pixel pitch an optical field, for example, r2 in FIG. 1, detected by a CCD detection unit, is influenced only by p1 and p2, and accordingly, r2 can be given as expressed in Equation 2.r2=∫ffd/2ffd/2[√{square root over (p2)}h(x−σ)+√{square root over (p1)}h(x−σ+1)]2dx  Equation 2
In this case, ffd is the fill factor of the detector, so that Equation 2 can be rearranged to be expressed by three terms as in the following Equation 3.r2=p2H00(σ)+2√{square root over (p1p2)}H01(σ)+p1H11(σ)  Equation 3,
wherein H00, H01 and H11 are the values of the optical fields detected at the detector pixels. If the above optical model is used, p2 can be obtained by the following Equation 4 on the assumption that p1 has been obtained. That is, the ON or OFF levels of the SLM at the pixels p0, p1 and p2, can be inversely calculated using the values of the optical fields detected by the detector. Therefore, even though misalignment of pixels occurs at the time of reproduction, an image detected by the detector can be corrected.
                              p          2                =                              1                                          H                00                            ⁡                              (                σ                )                                              ⁡                      [                                          -                                  (                                                                                    p                        1                                                              ⁢                                                                  H                        01                                            ⁡                                              (                        σ                        )                                                                              )                                            +                                                                                          p                      1                                        ⁡                                          (                                                                                                    (                                                                                          H                                01                                                            ⁡                                                              (                                σ                                )                                                                                      )                                                    2                                                -                                                  (                                                                                                                    H                                00                                                            ⁡                                                              (                                σ                                )                                                                                      ⁢                                                                                          H                                11                                                            ⁡                                                              (                                σ                                )                                                                                                              )                                                                    )                                                        +                                      (                                                                                            H                          00                                                ⁡                                                  (                          σ                          )                                                                    ⁢                                              r                        2                                                              )                                                                        ]                                              Equation        ⁢                                  ⁢        4            
However, the above-described image correction method for the misalignment of pixels using the optical model of Burr is problematic in that it takes lots of time to calculate original signal intensities passing through the SLM with the values of the optical fields detected at the detector pixels, thus decreasing an image data processing speed.
In the meantime, as another method for solving the problem of serious degradation of the data detected in the CCD array when the 1:1 pixel matching is applied, there has been proposed an oversampling method of oversampling a single pixel of an image reproduced from a storage medium into nine pixels in a CCD array and reconstructing only the data of a single center pixel among the nine pixel data as original data. This method is advantageous in that it has a small amount of calculation compared to the optical modeling method of Burr and can restore data relatively precisely, but is problematic in that it must oversample original image data at the time of reproduction, thus increasing the size of a CCD array.